English

$\left(\varphi_1, \varphi_2\right)-$Variational principle

Functional Analysis 2016-10-20 v1

Abstract

In this paper we prove that if XX is a Banach space, then for every lower semi-continuous bounded below function f,f, there exists a (φ1,φ2)\left(\varphi_1, \varphi_2\right)-convex function g,g, with arbitrarily small norm, such that f+gf + g attains its strong minimum on X.X. This result extends some of the well-known varitional principles as that of Ekeland [18], that of Borwein-Preiss [6] and that of Deville-Godefroy-Zizler [14, 15].

Keywords

Cite

@article{arxiv.1610.05915,
  title  = {$\left(\varphi_1, \varphi_2\right)-$Variational principle},
  author = {Abdelhakim Maaden and Abdelkader Stouti},
  journal= {arXiv preprint arXiv:1610.05915},
  year   = {2016}
}
R2 v1 2026-06-22T16:25:05.591Z